Reducing structural compliance by varying boundary conditions positions in topology optimization problems

Abstract

The paper investigates the influence of rational displacement of boundary conditions on the results of topological optimization of structures. It is shown that the traditional approach, which assumes a fixed position of loads and supports, may not consider a significant potential for improving the optimality criterion (minimization of compliance). A methodology is proposed, based on determining admissible displacement trajectories for boundary conditions along the lines of action of resultant forces while maintaining static equivalence of the system. A limited displacement zone is introduced for each condition, ensuring kinematic consistency of the mechanism. The method is implemented using the SIMP algorithm (TopOpt-2D) for a two-dimensional problem involving concentrated forces and hinged supports. The results of numerical simulation demonstrate that even a slight displacement of a single boundary condition within a given trajectory can reduce the compliance of the optimized topology by 15–29% while keeping the material volume constant. Comparison of the obtained topologies confirms their alignment with the displacement directions. It is concluded that preliminary refinement of boundary condition positions in the early design stages is highly effective. Further development of the method towards accounting for dynamic loads and automating the selection of positions is identified as a relevant task for future research.